Multiple discrete frequency ranging with error detection and correction

ABSTRACT

A range determination apparatus for determining target range within a range depth of D and within a range bin error of e comprises a carrier frequency transmitter for transmitting a carrier frequency and a generator for generating at least two modulating signals having frequency f 1  and f 2 , respectively. A modulation device, operative for at least two discrete frequencies for providing one of simultaneous or sequential modulated signals, is coupled to the carrier frequency transmitter for modulating the carrier. The two modulating frequencies and a common sub-multiple counting frequency are related such that f o  =m 1   &#39;  f 1  =m 2   &#39;  f 2 . A receiver is provided for receiving a reflected signal from the target and for producing a corresponding received electrical signal. A phase detection device is responsive to the modulating signals of the generator and the received signals for detecting the phase difference x 1   &#39;   and x 2   &#39; , respectively, between the modulating signals of the frequencies and each of the corresponding received signals. A data processor is coupled to receive the detected phase differences for each of the received signals.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is in the field of radar ranging and more particularly inthe field of error detection and correction in plural frequency rangingradar systems. The invention has application, for example, in guidancesystems, laser surveying and automatic camera focusing apparatus.

2. Description of the Prior Art

Radar ranging devices are based upon measurements of phase differencesbetween transmitted and received signals. Such systems suffer frommeasurement ambiguities resulting from the fact that phase is amultivalent function. In using high pulse repetition frequencies (PRF)in which the target range is greater than the equivalent distancebetween transmitted pulses, it is uncertain as to which transmittedpulse with which the received pulse is to be correlated. Multiple pulserepetition frequencies have been utilized to modulate the transmittedsignal in order to associate the return signal with the propertransmitted signal thus removing the ambiquity. Multiple, fixed PRF'shave been used to obtain accurate range data wherein sequentialmeasurements of the ambigious range corresponding to each PRF areobtained and compared to obtain the common range bin defining the rangeunambigiously. The PRF's are chosen to have a common submultiplefrequency. Range uniqueness is assured for certain pairwise relativelyprime harmonics of the counting frequency by the Chinese RemainderTheorem.

Reference is made to several prior art references, incorporated hereinby reference, namely Radar Handbook, by M. Skolnik, McGraw-Hill (1970),Chapter 19 and especially Section 19.3 and U.S. Pat. Nos. 3,277,473,4,106,019 and 3,649,123.

In making the range measurement for each PRF, small errors in any of themeasured phase shifts can give rise to catastrophic errors in thesynthesized or decoded range. Wide objects which fill several rangegates can also yield several valid phase measurements for eachfrequency, and thus yield widely different (and incorrect) decodedranges. Such range measurement errors develop not only in PRF systems,but in systems using other forms of modulation such as amplitudemodulation, pulse-width modulation, and frequency modulation. Thepresent invention uses amplitude modulation as an exemplary embodiment.

SUMMARY OF THE INVENTION

It is an object of the invention to provide a new and improved rangingapparatus and method to detect and correct errors in prior art systemsand methods.

Another object of the invention is to provide a radar ranging apparatusand method which is applicable to detect and correct small measurementerrors in multiple discrete PRF ranging devices.

Yet another object of the invention is to provide an improved rangingapparatus for use, for example, in aircraft or rocket guidance systems,laser surveying or automatic camera focusing devices.

A further object of the invention is to provide a radar ranging deviceand method applicable to obtain accurate and unambiguous range dataduring relatively short dwell times, as for example, in the order of 5microseconds/pixel at distances on the order of 500-5,000 ft and atresolutions on the order of about 1 ft. Such measurements arepreferably, but not necessarily, obtained using only two modulatingfrequencies in a discrete PRF system.

The invention is directed toward a range determination apparatus fordetermining target range within a range depth of D and within a rangebin error of e. I.e., it is assumed that the error in measuring themismatch of the return echo relative to the modulated frequency is nomore than e range bins, where the length of the range bin is defined asone-half the wavelength of the counting frequency. The apparatuscomprises (a) a carrier frequency transmitter for transmitting a carrierfrequency (b) means for generating at least two modulating frequenciesf₁ and f₂, (c) means coupled to the carrier frequency transmitter formodulations of the carrier either simultaneously or sequentially, (d)means to receive the reflected signals from the target, (e) means forfiltering the f₁ and f₂ frequencies from the received signal, (f) meansfor detecting the phase differences x₁ ', x₂ ' (measured in integralcounts of the period of the counting frequency f_(o)) between themodulating frequencies f₁ and f₂ and each of the corresponding filteredsignals, and (g) data processing means for processing the phasedifference signals to obtain the true target range. The at least twomodulating signals are related to one another such that

    f.sub.o =m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2

where

    m.sub.1 '=m.sub.1 m.sub.r

    m.sub.2 '=m.sub.2 m.sub.r

    m.sub.r ≧4e+1

    m.sub.1 m.sub.2 ≧D/m.sub.r

and where m₁, m₂ and m_(r) are pairwise relatively prime. f_(o) is thecounting frequency. The data processing means is operative

(1) to calculate ##EQU1## where R(x)_(m) is defined as the residue of xmodulo m.

(2) to compare R(x₁ ')_(m).sbsb.r with R(x₂ ')_(m).sbsb.r and if unequalto modify at least one of x₁ ' and x₂ ' by adding or subtracting aninteger≦e to produce modified phase differences x₁ " and x₂ " so thatresidues R(x₁ ")_(m).sbsb.r and R(x₂ ")_(m).sbsb.r of the modified phasedifferences are equal, and

(3) to decode one of (1) the residue number triplet [R(x₁ ')_(m).sbsb.1,R(x₂ ')_(m).sbsb.2, R(x₁ ')_(m).sbsb.r ] and

(2) the modified residue number triplet [R(x₁ ")_(m).sbsb.1, R(x₂")_(m).sbsb.2, R(x₁ ")_(m).sbsb.r ] relative to the module set[m₁,m₂,m_(r) ] to obtain the true target range.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in relation to the preferred embodiment andthe figures wherein:

FIG. 1 shows the phase shift between a transmitted and return echosignal;

FIG. 2 illustrates a range bin timing chart for the determination ofunambiguous ranges in a multiple discrete PRF ranging system;

FIG. 3 is a flow chart showing the computation steps utilized as part ofthe ranging system of the invention;

FIGS. 4A and 4B are block diagrams of a two frequency laser rangingsystem in accordance with the invention; and

FIG. 5 is a block diagram of a digital processing embodiment for FIG. 3.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The background principles for understanding the invention may bedescribed with reference to FIGS. 1 and 2. FIG. 1 illustrates graphs ofthe transmitted and received echo signals. A continuous waveform isshown in FIG. 1 although the same principles apply to pulsed waveforms.The transmitted signal having a frequency f₁ is used to modulate acarrier signal and is selected to have a frequency which is asub-multiple of a counting frequency f_(o). The counting frequency isused to count the phase difference between the transmitted and returnedecho signal. For example, f_(o) =m f₁, where m is an integer, e.g. 250.In FIG. 1, the pulse difference between the transmitted and returnedsignal is measured to be k periods of the counting frequency f_(o). Arange gate or bin has depth c/2f_(o), and the gates are numberedconsecutively from the source beginning with range bin 0. For the kcounts shown, the target range bin, defined as x, satisfies the relation

    x.tbd.k (modulo m).

Thus targets who range gates differ by a multiple of m areindistinguishable, and the measurement k is known as an ambiguous rangemeasurement. In FIG. 2, for example, the upper and middle charts showsthe choices for range bins possible assuming a modulating frequency,f_(o) =5 f₁ with a measured phase difference k=3. It may be seen thatthe true range bin can not be determined from the possible choices of3,8, 13, 18, 23 or 28. Averaging repeated measurements of the phaseshift (using, e.g., zero crossing detection or quadrature detection)reduces signal noise, thus increasing the confidence of the measurement.However, the range ambiguity remains.

One type of conventional laser ranging which removes range ambiguityassumes a maximum detection distance D and commences by amplitudemodulating the signal at a frequency f₁ of wavelengthλ≧2D, with acounting frequency f₁ '=N f₁ for some integer N, typically N=256. Thispartitions [O,D] into N equal range bins, and the phase measurementunambiguously determines the range bin of the target. To improve therange resolution, the process is repeated with higher frequencies:

    f.sub.2 =Nf.sub.1

    f.sub.2 '=Nf.sub.2

(the new counting frequency)

and, in general,

    f.sub.i =Nf.sub.i-1

    f.sub.i '=Nf.sub.i,

repeated until the resolution specifications are met.

A disadvantage of such systems are their limited applicability. Forexample, if it is desirable to measure target range over an intervalbetween 500 and 5,000 feet with a 5 microsecond dwell time per pixel andan accuracy of 1 foot, the conventional ranging system would select thefirst or lowest frequency modulation to have a wavelength of 2D=2(5,000-500)=9000 feet. The period for such a wavelength is about 9microseconds which exceeds the 5 microsecond desired dwell, so that theconventional system is inapplicable.

The present invention is based upon another prior art technique, namely,the multiple discrete PRF ranging technique also illustrated inreference to FIGS. 1 and 2. Given a desired distance resolution (ormaximum distance error) d₀, the counting frequency f₀ is chosen suchthat λ₀ =c/f₀ =2d₀. Modulation frequencies f₁, f₂, . . . ,f_(s) arechosen so that f₀ =m_(i) f_(i), where the m_(i) are pairwise relativelyprime integers. Phase measurements k₁, . . . ,k_(s) are performed asdescribed above, and, if no measurement errors occur, the true range binx satisfies

    k.sub.i .tbd.x.sub.i (modulo m.sub.i)--(i=1,2, . . . ,s).

The Chinese Remainder Theorem asserts the existence of a unique integerx, ##EQU2## satisfying this system of congurences; and hence the rangefor any target in the bins numbered 0 up to (but not including) ##EQU3##can be unambiguously determined.

An example of known multiple discrete PRF ranging is given as follows.Let f_(o), f₂ be chosen such that f_(o) =5 f₁ =6 f₂. Assume the phasemeasurements yield 3 for the PRF of f₁ and 5 for the PRF of f₂establishing the following pair of congruences for the range bin x:

    x.tbd.3 (mod 5)

    x.tbd.5 (mod 6).

According to the Chinese Remainder Theorem, there exist a unique integerbetween 0 and 29 (5×6-1) which satisfies the simultaneous consequences.

Decoding schemes exist to determine the unique number but the answer mayreadily be seen by reference to FIG. 2. The measured phase shifts of 3for the f, (modulo 5) transmission lines up with the measured phaseshift of 5 for the f₂ (modulo 6) transmission at only one range binwithin the poissible ranges of 0-29, namely range bin 23. Thus, themeasured target range is determined unambigiously.

The difficulty with conventional multiple discrete PRF ranging, and theproblem to which the invention is directed, is illustrated using thesame example as above. Now, however, it is assumed that there is ameasurement error so that the phase difference for the modulationfrequency f₁ is measured to be 2 instead of 3, e.g. a phase error of onerange bin. Thus, ##EQU4##

From FIG. 2 the results can be seen that the range bin 17 provides theonly unique solution to the above two congruences for values 0≦x<29.Range bin 17, however, is a large error from the true range bin 23. Itmay thus be appreciated that a fundamental problem in prior art rangingis that small measurement errors (i.e., one bin, for example) can resultin large or even catastrophic errors in the range bin result. Theproblem is even more acute when one realizes that such phase measurementerrors are to be expected since basically, the measurement of phaseforces a continuous range value into one of a finite plurality ofdiscrete bins. Such discretization can easily cause measurement errors.The invention is associated with and implemented by a choice of discretefrequencies and associated moduli for a ranging system; hence, theinvention is not simply an "add-on" to an existing system. While thepreferred form of the laser system uses only two frequencies, thetechnique is applicable to and is described for arbitrarily manyfrequencies. The transmitted signal can either be simultaneouslymodulated at all frequencies (as in the preferred laser system) or thefrequency modulations and phase measurements can be sequentiallyperformed.

The notation R(x)_(m) will denote the residue of x modulo m. For x≧0,R(x)_(m) is the remainder upon dividing x by m. A more generaldefinition which applies to negative as well as positive integers x isas follows: R(x)_(m) is the unique integer in the interval 0≦R(x)_(m) <mfor which x-R(x)_(m) is a multiple of m. The notation A(x) will be usedto denote the absolute value of x.

The ranging technique in accordance with the invention requires thefollowing two propositions. Proposition 1 is well known and is statedwithout proof.

Proposition 1. If the m and n are integers with n a multiple of m, thenfor any integer x,

    R(x).sub.m =R(R(x).sub.n).sub.m.

Proposition 2. If the x, y, and m are integers such that A(x-y)≦(m-1)/2,then A(x-y)=min (R(x-y)_(m), m-R(x-y)_(m)). ##EQU5## SinceA(x-y)≧(m-1)/2 and exactly one of the two values R(x-y)_(m) andm-R(x-y)_(m) is no greater than (m-1)/2, A(x-y) must equal the smallerof these two values.

Also used throughout the discussion is the fundamental fact upon whichthe Residue Number System (RNS) is based: a sum, difference, or productof integers which is then reduced modulo m is congruent (modulo m) tothe sum, difference, or product, respectively, of their modulo mresidues.

Choice of frequencies and moduli

Assume is frequencies are to be used and the maximum absolute bin errorin measuring the ambiguous range bins is an integer e≧0. As will beseen, the decoded range bin will differ from the true distance by nomore than e bins. Let D represent the total range depth desired. Forexample, in the preferred laser system: s=2, e=1, D=4500 feet, and thedecoded distance will have an error of at most 1 foot, which is thelength of one range bin.

Let m_(r) be an integer satisfying m_(r) ≧4 e+1, and choose integers m₁,m₂, . . . ,m_(s) which are pairwise relatively prime, each relativelyprime to m_(r), and ##EQU6## The modulus m_(r) will be incorporated as aredundant modulus, but no redundant frequency need be associated withit. Next, let m₁ '=m_(i) m_(r), i=1 . . . ,s. Given the countingfrequency f₀, the discrete frequencies f_(i), i=1 . . . ,s are chosen sothat

    f.sub.0 =m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 = . . . =m.sub.s 'f.sub.s

Let x represent the true range bin for the target, and let x_(i)'represent the ambiguous range measurements corresponding to f_(i), i=1,. . . ,s. If no measurement errors are encountered, then x_(i)'=R(x)_(m).sbsb.i ' for i=1, . . . ,s. Proposition 1 then implies that

    R(x.sub.1 ').sub.m.sbsb.r =R(x.sub.2 ').sub.m.sbsb.r = . . . =R(x.sub.s ').sub.m.sbsb.r

since each m_(i) ' is a multiple of m_(r). Since errors are assumed, themeasured values x_(i) ' actually have the form

    x.sub.i '=R(x+a.sub.i).sub.m.sbsb.i '

for unknown integers a_(i) with A(a_(i))≦e. The s-tuple (x₁ ' x₂ ', . .. ,x_(s) ') represents legitimate range bin if and only if the valuesR(x_(i) ')_(m).sbsb.r are all equal. This implies a₁ =a₂ = . . . =a_(s)and the values (R(x₁ ')_(m).sbsb.1, R(x₂ ')_(m).sbsb.2 . . . R(x_(s)')_(m).sbsb.s, R(x_(i) ')_(m).sbsb.r) are decoded relative to the moduliset (m₁,m₂, . . . ,m_(s),m_(r)), yielding x+a for the computed range bin(differing from the true range bin by no more than (e), where a is thecommon value of the a_(i).

If a legitimate range bin is not found, an error is detected, and theprocedure for error correction is given by the following five steps.

Step 1

Compute

    x.sub.i =R(x.sub.i ').sub.m.sbsb.i (=R(x+a.sub.i).sub.m.sbsb.i)

and

    x.sub.i.sup.r =R(x.sub.i ').sub.m.sbsb.r (=R(x+a.sub.i).sub.m.sbsb.r) for i=1,2, . . . ,s.

These computations may be performed via table look-up with programmableread only memories (PROMs). The moduli set (m₁,m₂, . . . ,m_(s),m_(r))will form the basis for decoding once the corrected residue relative toeach modulus is determined.

Step 2

For each distinct pair of indices i,j, i=1,2, . . . ,s, j=1,2, . . . ,s,compute

    d(i,j)=min(R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r, m.sub.r -R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r)

and choose i₀, j₀ at which d(i₀,j₀) is maximal.

By Proposition 2, d(i₀,j₀) is the maximum absolute difference betweenany pair of unambiguous range values (x+a_(i)) and (x+a_(j)).

Step 3

Choose an integer y, 0≦y<m_(r) as follows:

    y=R(x.sub.j.sbsb.0.sup.r +[R(x.sub.i.sbsb.0.sup.r -x.sub.j.sbsb.0.sup.r).sub.m.sbsb.r /2]).sub.m.sbsb.r if R(x.sub.i.sbsb.0.sup.r -x.sub.j.sbsb.0.sup.r).sub.m.sbsb.r ≦2e, (a)

    y=R(x.sub.i.sbsb.0.sup.r +[R(x.sub.j.sbsb.0.sup.r -x.sub.i.sbsb.0.sup.r).sub.m.sbsb.r /2]).sub.m.sbsb.r if R(x.sub.j.sbsb.0.sup.r -x.sub.i.sbsb.0.sup.r).sub.m.sbsb.r ≦2e, (b)

where [ ] denotes the greatest integer function.

By Proposition 2 and the assumption that A(a_(i))≦e, either thehypothesis of (a) or (b) must hold. Also, the quantities within thegreatest integer functions are no greater than e. Conceptually, y hasbeen chosen approximately midway "between" x_(i).sbsb.0^(r) andx_(j).sbsb.0^(r) in the ring of integers moduli m_(r).

Step 4

Compute b_(i), i=1, . . . ,s according to

    b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r ≦e, and

    bi=R(x.sub.i.sup.r -y).sub.m.sbsb.r -m.sub.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r >e.

Either R(x_(i) ^(r) -y)_(m).sbsb.r ≦e or m_(r) -R(x_(i) ^(r)-y)_(m).sbsb.r ≦e,

and hence A(b_(i))≦e. Next it is claimed that a_(i) -b_(i) is a constantindependent of i. Since A(a_(i))≦e,-2e≦a_(i) -b_(i) ≦2e. Since m_(r)≧4e+1 (which, in turn is greater than the length of the interval inwhich a_(i) -b_(i) must lie), it suffices to show that R(a_(i)-b_(i))_(m).sbsb.r is a constant: ##EQU7## using the definitions ofb_(i) and x_(i) ' and Proposition 1.

Let d'=a_(i) -b_(i) denote this common difference.

Step 5

Form the differences x_(i) *=R(x_(i) -b_(i))_(m).sbsb.i and decode (x₁*, x₂ *, . . . ,x_(s) *, y).

This decoded value is the unambiguous range bin and actually equalsx+d'. To show this, it suffices to show that ##EQU8## For the former,##EQU9## and for the latter, ##EQU10## It remains to show that d'≦e,which verifies that the decoded unambiguous range bin differs from thetrue range bin by no more than e bins. Note that by Proposition 2,either

    x.sub.i.sbsb.0.sup.r, R(x.sub.i.sbsb.0.sup.r +1).sub.m.sbsb.r, R(x.sub.i.sbsb.0.sup.r +2).sub.m.sbsb.r, . . . , x.sub.j.sbsb.0.sup.r

or

    x.sub.j.sbsb.0.sup.r, R(x.sub.j.sbsb.0.sup.r +1).sub.m.sbsb.r, R(x.sub.j.sbsb.0.sup.r +2).sub.m.sbsb.r, . . . , x.sub.i.sbsb.0.sup.r

forms a set of no more than 2 e contiguous integers in the ring ofintegers modulo m_(r) (considering m_(r) -1 and 0 to be contiguous).This set must contain the integer y, which has been chosen in Step 3 tobe no more than e positions from either endpoint. Also, this set mustcontain R(x)_(m).sbsb.r (the modulo m_(r) residue of the true range bin)which also must be no more than e positions from either endpoint. Hencey and R (x)_(m).sbsb.r can be no more than e positions apart. ApplyingProposition 2 twice, (once for a_(i) and b_(i), once for y andR(x)_(m).sbsb.r), it follows that

    A(d')=A(a.sub.i -b.sub.i)=A(y-R(x).sub.m.sbsb.r)≦e.

The following examples demonstrate the computational simplicity of thealgorithm.

EXAMPLES

Assume the maximum measurement error e equals 1 range bin, so that m_(r)=4e+1=5. Let the total number of discrete frequencies (i.e., the numberof moduli) be s=2, and choose m₁ =7, m₂ =11. Then m₁ '=35, m₂ '=55, andrange bins from 0 through 5×7×11-1=384 can be unambiguously determined.Assume the true range bin for the target is x=215. ##EQU11## Since x₁^(r) =x₂ ^(r) the triple (x₁,x₂,x₁ ^(r))=(5,6,5) is decoded relative tothe moduli set (m₁,m₂,m_(r)) to obtain 215.

(b) Measurement: (x₁ ', x₂ ')=(5,51)

    x.sub.1 =R(5).sub.7 =5 x.sub.2 =R(51).sub.11 =7

    X.sub.1.sup.r =R(5).sub.5 =0 x.sub.2.sup.r =R(51).sub.5 =1

Correction may proceed in one of two ways: (i) the integer 1 may beadded to x₁ and x₁ ^(r) and the triple (6,7,1) decoded to obtain 216; or(ii) the integer 1 may be subtracted from x₂ and x₂ ^(r) and the triple(5,6,0) decoded to obtain 215. On the first instance, a small rangeerror is obtained, and in the second case, no error is obtained. Anotherway to visualize the solution is to modify x₁ ' and x₂ ' by adding orsubtracting an integer≦e to obtain x₁ " and x₂ " such that R(x₁")_(m).sbsb.r =R(x₂ ")_(m).sbsb.r. The triplet R(x₁ ")_(m).sbsb.1, R(x₂")_(m).sbsb.2 and R(x₁ ")_(m).sbsb.r =R(x₂ ")_(m).sbsb.r is then decodedrelative to the moduli set (m₁,m.sub. 2,m_(r)). ##EQU12##

A legitimate range bin is found, and (6,7,1) is decoded to 216 for anerror of one range bin. ##EQU13## A common value for x₁ ^(r) and x₂ ^(r)must be obtained by adding or subtracting 1 (since e=1) to one or bothvalues. Since x₁ ^(r) +1=0 (mod 5) and x₂ ^(r) -1=0 (mod 5), (R(x₁ +1)₇,R(x₂ -1)₁₁, 0)=(5,6,0) is decoded to obtain 215, the true range bin.

A specific example applicable for the preferred system for a range depthof 4,500 feet with a dwell time of 5 microseconds with 1 foot resolutionutilizes the following parameters. The counting frequency f_(o) isapproximately 492 MHz and a maximum one count error for each of the twofrequencies gives e=1 with m_(r) =5. Additionally, one may select m₁=19, m₂ =49 such that m₁ '=95 and m₂ '=245. The maximum range is thenm_(r) m₁ m₂ =4655 and the modulating frequencies are given by

    f.sub.1 =f.sub.o /m.sub.1 '=5.18 MHz

    f.sub.2 =f.sub.o /m.sub.2 '=2.01 MHz.

Another specific example applicable for yet another preferred embodimentuses a range depth of 2070 feet with a dwell time of 5 microseconds with1 foot resolution and utilizes the following parameters. The countingfrequency is approximately 463 MHz and a maximum two count error foreach of the two frequencies gives e=2 and m_(r) =10. Additionally, onemay select m₁ =9, m₂ =23 such that m₁ '=90 and m₁ '=230. The maximumrange is then m_(r) m₁ m₂ =2070 and the modulating frequencies are givenby

    f.sub.1 =f.sub.o /m.sub.1 '=5.144 MHz

    f.sub.2 =f.sub.o /m.sub.2 '=2.013 MHz.

These specific parameters are utilized in the block diagram of FIG. 4.It is pointed out that the selection of two modulating frequencies inthe preferred embodiment is made so as to enable use of conventionallaser systems where power consumption demands make larger numbers offrequencies presently unpractical. However, with larger dwell times orlaser systems employed in devices which have large power reserves, morethan two frequencies may readily be used.

It may also be appreciated that use of the redundant modulus m_(r)without the need for an extra transmitted redundant modulating frequencyprovides a distinct advantage of the present system over the prior artespecially in environments where electrical power must be frugallyemployed. It is not absolutely necessary to select the modulatingfrequencies by choosing integers (viz., m_(r), m₁, m₂, etc.) which arepairwise relatively prime. Integral multiples of the modlui (i.e., k₁ m₁m_(r), k₂ m₂ m_(r), etc., for integers k₁, k₂ ; etc.) may also be usedfor the sake of selecting the modulating frequencies wherein

    f.sub.o =f.sub.1 k.sub.1 m.sub.1 m.sub.r =f.sub.2 k.sub.2 m.sub.2 m.sub.r =(etc.).

The data processing of the phase measurements x₁ ', x₂ ', etc., arefirst reduced modulo m₁ m_(r), m₂ m_(r), respectively, etc., and maythen proceed as described above where the residue number representationis decoded with respect to the moduli set (m₁, m₂, . . . , m_(r)).

The process of decoding the triplets (x₁,x₂,x₁ ^(r)) relative to themoduli set (m₁,m₂,m_(r)) may be done using a mixed radix conversionprocess such as described in the test of Nicholas S. Szabo and RichardL. Tanaka, entitled Residue Arithmetic and Its Applications to ComputerTechnology, McGraw-Hill (1967), Section 3-6. Another section of theabove text is of interest for its treatment of the Chinese RemainderTheorem namely Section 2-4. Yet another reference of interest for itsteaching of redundant number systems for use in error detection andcorrection in digital filters, and its teaching of mixed radix digitsand the redundant residue number system, is the publication of Mark H.Etzel and W. Kenneth Jenkins "Redundant Residue Number Systems for ErrorDetection and Correction in digital Filters," IEEE Transactions inAcoustics, Speech, and Signal Processing, Vol ASSP-28, No. 5, October1980. Both of the publications are incorporated herein by reference.

A flowchart which illustrates the steps 1-5 discussed above is given inFIG. 3. Steps 1-5 as shown in the flowchart correspond to the steps 1-5set forth above.

FIGS. 4 and 5 illustrate the hardware utilized in practicing theinvention for a two frequency laser ranging system. The transmitting andreceiving apparatus is seen to comprise a CO₂ laser 101, beam splitter103, an acousto-optic frequency shifter 105, RF driver 107, electrooptic AM modulators 109, beam splitters 111 and 113, mirror 115, anddownstream detection, filtering and phase detection apparatus. Themodulating frequencies of 2.008 MHz and 5.180 MHz are derived from asingle 491.96 MHz (the counting frequency f_(o)) crystal oscillatorsource 117 via frequency divide circuits 119 and 121 respectively. Themodulating frequencies are fed to respective electro optic modulatordrive circuits 123 and 125 which in turn drive the electro optic AMmodulator 109. In the preferred embodiment, simultaneous 2.008 MHz and5.180 MHz modulations are applied due to the short dwell time and rangeparameters of the desired system. However, sequential modulation isclearly possible in a more general case. The acousto-optic frequencyshifter 105 may be fabricated from two serially connected 40 MHz unitswith the R.F. driver 107 being operated at 40 MHz to provide a totalfrequency modulation of the lasar beam of 80 MHz. The CO₂ laserfrequency is typically 3×10¹³ Hz.

The beam splitter 103 serve to produce a local oscillator beam passingto mirror 115 and a transmitted beam passing through the acousto-opticfrequency shifter 105 and the AM modulators 109. The transmitted beampassing straight through beam splitter 111 is thus frequency shifted byan amount ±80 MHz and AM modulated by the two frequencies f₁ =2.008 MHzand f₂ =5.180 MHz. Subsequent to passage through the beam splitter 111,the transmitted beam may pass through a convention beam expander,collimater optics and scanner all generally indicated at 131.

The return signal passes to beam splitter 111 and then to beam splitter113 where it is combined with the unshifted local oscillator beam toproduce a beat note at 80 MHz. The 80 MHz signal acts as an IF carrierto the f₁ and f₂ AM modulating frequencies.

The downstream detection, filtering and phase detection apparatuscomprises a HgCdTe detector 133 (biased by a bias control circuit 134)which produces the modulated IF carrier signal, a 80 MHz centerfrequency bandpass filter 135, and a demodulating envelope detector 137.A switch SW is provided to enable automatic or manual gain control (AGCor MGC) as indicated. There is further provided a low pass filter 139(10 MHz cutoff) and bandpass filters 141 and 143 with f₁ and f₂ ascenter frequencies respectively. The separate f₁ and f₂ signals aresubsequently fed to respective zero crossing phase detectors 145 and147. The phase detectors 145 and 147 digitally compare the returnfiltered signals with the untransmitted modulator drive signals f₁ andf₂ to produce binary coded phase values which are subsequently fed to aresidue processor 149.

The residue processor 149 may take the form of a conventionalprogrammable digital computer including a CPU, RAM, ROM, and I/Ochannels as shown in block form in FIG. 5. The ROM stores a programdesigned to implement the flowchart of FIG. 3. The digital processor mayalso be of a special purpose LSI fabrication suitable to provide thetrue range data for use in missile guidance, laser surveying and camerafocusing applications as non-limiting examples.

In such a case or as an alternative to the CPU configuration in FIG. 5,hardwired logic circuitry may be devised in combination with a pluralityof PROMs to perform the necessary data processing.

It should also be pointed out that with regard to FIGS. 4A and 4B thatif sequential modulation of the carrier frequency is utilized, thebandpass filters 141 and 143 would not be required and only at least onephase detector circuit would be required inasmuch as the time separationof the modulated signals will serve to differentiate them.

What is claimed is:
 1. Range determination apparatus for determiningtarget range within a range depth of D and within a range bin error of ecomprising:(a) a carrier frequency transmitter for transmitting acarrier frequency, (b) means for generating at least two modulatingsignals having frequency f₁ and f₂ respectively, (c) modulation meanscoupled to said carrier frequency transmitter for modulating saidcarrier, said modulation means operative for said at least two discretefrequencies f₁ and f₂ for providing one of simultaneous or sequentialmodulated signals, (d) said at least two modulating frequencies and acommon sub-multiple counting frequency f_(o) related such that

    f.sub.o m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2

where,

    m.sub.1 '=m.sub.1 m.sub.r

    m.sub.2 '=m.sub.2 m.sub.r

    m.sub.r ≧4e+1

    m.sub.1 m.sub.2 ≧D/m.sub.r

and where m₁,m₂ and m_(r) are pairwise relatively prime, (e) a receiverfor receiving a reflected signal from said target and for producing areceived electrical signal corresponding thereto, (g) phase detectionmeans responsive to said modulating signals of said generating means andsaid received signals for detecting the phase difference x₁ ' and x₂ 'respectively between the modulating signals of frequencies f₁ and f₂ andeach of the corresponding received signals, (h) data processing meanscoupled to receive said detected phase differences for each of saidreceived signals, said data processing means operative (1) to calculate##EQU14## where R(x)_(m) is defined as the residue of x modulo m, (2) tocompare R(x₁ ')_(m).sbsb.r with R(x₂ ')_(m).sbsb.r and if unequal tomodify at least one of x₁ ' and x₂ ' by adding or subtracting aninteger≦e to produce modified phase differences x₁ " and x₂ " so thatresidues R(x₁ ")_(m).sbsb.r and R(x₂ ")_(m).sbsb.r of the modified phasedifferences are equal, and (3) to decode one of (1) the residue numbertriplet [R(x₁ ')_(m).sbsb.1, R(x₂ ')_(m).sbsb.2, R(x₁ ')_(m).sbsb.r ]and the modified residue number triplet [R₁ ")_(m).sbsb.1, R(x₂")_(m).sbsb.2, R(x₁ ")_(m).sbsb.r ] relative to the moduli set[m₁,m₂,m_(r) ] to obtain the target range.
 2. Range determinationapparatus as recited in claim 1 wherein said data processing meanscomprises a programmable digital computer.
 3. Range determinationapparatus as recited in claim 1 wherein said carrier frequencytransmitter comprises a laser.
 4. Range determination apparatus asrecited in claim 1 wherein said modulation means is operative tosimultaneously modulate said carrier frequency.
 5. Range determinationapparatus as recited in claim 1 wherein said modulation means isoperative to sequentially modulate said carrier frequency.
 6. Rangedetermination apparatus as recited in claim 1 wherein f_(o) is about 500MHz, m_(r) =5, f₁ is about 5 MHz, and f₂ is about 2 MHz.
 7. A method fordetermining the true target range within a range depth of D and within arange bin error of e from multiple pulse repetition frequencies of radarcomprising the steps of:a. transmitting signals having at least twodistinct frequencies f₁ and f₂, b. said frequencies related to eachother and to a counting frequency f_(o) such that

    m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 =f.sub.o

where

    m.sub.1 '=m.sub.1 m.sub.r

    m.sub.2 '=m.sub.2 m.sub.r

    m.sub.r ≧4e+1

    m.sub.1 m.sub.2 ≧D/m.sub.r

and where m₁, m₂ and m_(r) are pairwise relatively prime, c. receivingreflected echo signals from said target for each frequency f₁ and f₂, d.detecting the difference in phase difference x₂ ', x₂ ' respectivelybetween the transmitted and received signals for each frequency f₁ andf₂, e. calculating in response to said phase differences x₁ ', x₂ ' theresidues,

    R(x.sub.1 ').sub.m.sbsb.1    , R(x.sub.2 ').sub.m.sbsb.2

    R(x.sub.1 ').sub.m.sbsb.r    , R(x.sub.2 ').sub.m.sbsb.r

f. comparing R(x₁ ')_(m).sbsb.r and R(x₂ ')_(m).sbsb.r, and if unequal,modifying at least one of x₁ ' and x₂ ' by adding or subtracting aninteger≧e to produce a modified phase difference x₁ ", x₂ " such thatresidues R(x₁ ")_(m).sbsb.r and R(x₂ ")_(m).sbsb.r of the modified phasedifferences are equal, and g. decoding one of (1) the residue numbertriplet [R(x₁ ')_(m).sbsb.1, R(x₁ ')_(m).sbsb.2, R(x₁ ')_(m).sbsb.r ] ifR(x₁ ')_(m).sbsb.r is equal to R(x₂ ')_(m).sbsb.r in step f and (2) themodified residue number triplet [R(x₁ ")_(m).sbsb.1, R(x₂ ")_(m).sbsb.2,R(x₁ ")_(m).sbsb.r ] if R(x₁ ')_(m).sbsb.r is not equal to R(x₂')_(m).sbsb.r in step f., each triplet decoded relative to the moduliset [m₁, m₂, m_(r) ] to obtain the true target range.
 8. A method fordetermining the true target range within a range depth D and within arange bin error e from multiple modulated frequencies of radarcomprising the steps of:(a) transmitting a plurality of distinctfrequencies f₁, f₂ . . . f_(i) . . . f_(s), (b) said plurality offrequencies related such that, for i=1, 2, . . . s,

    m.sub.1 'f.sub.1 =m.sub.2 'f.sub.2 =m.sub.1 'f.sub.i

where ##EQU15## where the m_(i) 's are pairwise relatively prime, (c)receiving reflected echo signals from said target for each frequencyf_(i), i=1,2, . . . s, (d) detecting the phase difference x₁ 'respectively between the transmitted and received signals for eachfrequency f_(i), i=1,2 . . . s, (e) calculating in response to each x₁', the residues ##EQU16## (f) for each distinct pair of indices i,jwhere i=1,2 . . . s and j=1,2 . . . s, computing,

    d(i,j)=min(R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r, m.sub.r -R(x.sub.i.sup.r -x.sub.j.sup.r).sub.m.sbsb.r)

and choosing i_(o), j_(o) at which d (i_(o),j_(o)) is maximal, (g)selecting integer y, o≧y<m_(r) as one of:

    y=R(x.sub.j.sbsb.0.sup.r +[R(x.sub.i.sbsb.0.sup.r -x.sub.j.sbsb.0.sup.4).sub.m.sbsb.r /2].sub.m.sbsb.r

if R(x_(i).sbsb.0^(r) -x_(j).sbsb.0^(r))_(m).sbsb.r ≧2e, and

    y=R(x.sub.i.sbsb.0.sup.r +[R(x.sub.j.sbsb.0.sup.4 -x.sub.i.sbsb.0.sup.r).sub.m.sbsb.r /2])

if R(x_(j).sbsb.0^(r) -x_(i).sbsb.0^(r))_(m).sbsb.r ≦2ewhen [ ] denotesthe greatest integer functions, (h) computing b_(i), i=1,2, . . . s suchthat

    b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r ≦e,

and

    b.sub.i =R(x.sub.i.sup.r -y).sub.m.sbsb.r -m.sub.r if R(x.sub.i.sup.r -y).sub.m.sbsb.r >e,

(i) subtracting x_(i) -b_(i) to form the differences

    x.sub.i.sup.* =R(x.sub.i -b.sub.i).sub.m.sbsb.i

i=1,2, . . . S, and (j) decoding the set (x₁ ^(*), x₂ ^(*) . . . x_(i)^(*) . . . x_(s) ^(*), y)relative to the moduli set (m₁, m₂ . . . m_(i). . . m_(s), m_(r)) to find the true target range.
 9. Rangedetermination apparatus is recited in claim 1 further comprising meansfor filtering each of said frequencies f₁ and f₂ from said receivedsignal to provide corresponding filtered signals, and wherein said phasedetection means is responsive to said filtered signals for detecting thephase difference x₁ ' and x₂ ' respectively between the modulatingsignals of frequencies f₁ and f₂ and each of the corresponding filteredsignals.